Thermal states of two identical two-level atoms interacting with the single-mode fields of the Arik–Coon and Biedenharn–Macfarlane q-oscillators

We consider the Jaynes–Cummings models (JCMs) of two identical two-level atoms interacting with a single mode of the Arik–Coon and Biedenharn–Macfarlane [Formula: see text]-boson fields in a cavity. It is shown that there is a constant of motion, so-called the total number of excitation, which leads to decomposition of the total Hilbert space of [Formula: see text]-deformed system into three invariant subspaces. So, we have the block diagonal structure with three blocks as the Hamiltonian matrices. The exact energy spectrum and eigenstates of the [Formula: see text]-deformed models are obtained by diagonalizing each block. Assuming that the cavity fields and atoms are in thermal equilibrium, the partition function and thermal density matrix of the models are calculated. Finally, the influence of deformation parameters of the Arik–Coon and Biedenharn–Macfarlane [Formula: see text]-oscillator light fields at low-temperatures on the entropy and internal energy of the Jaynes–Cummings models as well as on the atom–atom entanglement via the concurrence measure is analyzed.